High order quantum decoherence via multi-particle amplitude for boson system

In this paper we depict the high order quantum coherence of a boson system by using the multi-particle wave amplitude, whose norm square is just the high order correlation function. This multi-time amplitude can be shown to be a superposition of several "multi-particle paths". When the environment or a apparatus entangles with them to form a generalized "which-way" measurement for many particle system, the quantum decoherence happens in the high order case dynamically. An explicit illustration is also given with an intracavity system of two modes interacting with a moving mirror.